# Quantile-based fuzzy C-means clustering of multivariate time series: Robust techniques

arXiv: https://arxiv.org/abs/2109.11027 · HTML: https://mlsanity.com/paper/2109.11027/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 83 references that are in the map.
- First posted on arXiv 22 Sep 2021.

## Builds on (most cited first, 5 of 5)

- [A review on outlier/anomaly detection in time series data](https://mlsanity.com/paper/2002.04236/) (2020)
- [Dynamic Covariance Models for Multivariate Financial Time Series](https://mlsanity.com/paper/1305.4268/) (2013)
- [Quantile-based fuzzy clustering of multivariate time series in the frequency domain](https://mlsanity.com/paper/2109.03728/) (2021)
- [Model-based fuzzy time series clustering of conditional higher moments](https://mlsanity.com/paper/2104.00271/) (2021)
- [Robust Clustering for Time Series Using Spectral Densities and Functional Data Analysis](https://mlsanity.com/paper/1702.02165/) (2017)

## Built on by (most cited first, 6 of 6)

- [FCPCA: Fuzzy clustering of high-dimensional time series based on common principal component analysis](https://mlsanity.com/paper/2505.07276/) (2025)
- [Time series clustering based on prediction accuracy of global forecasting models](https://mlsanity.com/paper/2305.00473/) (2023)
- [Robust fuzzy clustering for high-dimensional multivariate time series with outlier detection](https://mlsanity.com/paper/2510.26982/) (2025)
- [Fuzzy clustering of ordinal time series based on two novel distances with economic applications](https://mlsanity.com/paper/2304.12249/) (2023)
- [Fuzzy clustering of circular time series based on a new dependence measure with applications to wind data](https://mlsanity.com/paper/2402.08687/) (2024)
- [Robust Spectral Fuzzy Clustering of Multivariate Time Series with Applications to Electroencephalogram](https://mlsanity.com/paper/2506.22861/) (2025)

## Abstract (arXiv)

Three robust methods for clustering multivariate time series from the point of view of generating processes are proposed. The procedures are robust versions of a fuzzy C-means model based on: (i) estimates of the quantile cross-spectral density and (ii) the classical principal component analysis. Robustness to the presence of outliers is achieved by using the so-called metric, noise and trimmed approaches. The metric approach incorporates in the objective function a distance measure aimed at neutralizing the effect of the outliers, the noise approach builds an artificial cluster expected to contain the outlying series and the trimmed approach eliminates the most atypical series in the dataset. All the proposed techniques inherit the nice properties of the quantile cross-spectral density, as being able to uncover general types of dependence. Results from a broad simulation study including multivariate linear, nonlinear and GARCH processes indicate that the algorithms are substantially effective in coping with the presence of outlying series (i.e., series exhibiting a dependence structure different from that of the majority), clearly poutperforming alternative procedures. The usefulness of the suggested methods is highlighted by means of two specific applications regarding financial and environmental series.